Wheel loaders and other work vehicles comprise an engine, travel wheels rotatably driven by driving force from the engine, and a power transmission mechanism for transmitting the driving force from the engine to the travel wheels. The power transmission mechanism has a transmission and a torque converter with a lock-up clutch, and a control unit controls the engaging and disengaging of the lock-up clutch and the shifting of gears in the transmission. For example, in the work vehicle shown in Japanese Laid-Open Patent Application No. 2007-107651, the transmission speed gear can be shifted from a first speed gear to a fourth speed gear, and the lock-up clutch can be switched between an engaged and a not-connected state. In a conventional work vehicle, the switching of the lock-up clutch between the engaged and not-connected state is determined according to whether or not the vehicle velocity is equal to or greater than a predetermined velocity. Specifically, when the vehicle velocity has reached a predetermined velocity or greater, the lock-up clutch is engaged and the driving force from the engine is transmitted to the transmission via the lock-up clutch.